本研究探討臺灣與美國中學數學職前教師數學語言相關教學思維，以及兩個國家職前教師在數學語言相關教學能力上的表現。
研究樣本為兩個國家在數學師資培育跨國研究（Teacher Education and Development Study in Mathematics, TEDS-M）樣本的子集（sub-sample），由臺灣、美國分別在其全體樣本中隨機抽出，共有161名臺灣中學數學職前教師、172位美國中學數學職前教師參與研究。
本研究發現，兩國職前教師思維中能連結到之文字敘述數學語言的特徵，都是較為一般性、整體性的描述，例如，抽象、冗長等，並不能做更深入、考量語句組成的分析。然而，分析他們實際提供給學生語句時，卻可發現他們認為學生易理解的語句應具有較程序性，例如，以運算動作取代大量名詞化、提供可操作之具體物件，較低數學專門用語的使用量，較口語化，訊息進展速度較緩慢等等特徵。本研究發現在數學語言相關教學能力表現上，臺灣職前教師在「執行」及「推理與判斷」方面較美國職前教師優異，而兩個國家在「執行」方面的表現都優於「推理與判斷」方面的表現。上述教學思維與教學能力的現象都反映出職前教師思維中所連結的概念，乃屬於Schön（1983）提出無聲的（tacit）、實踐的知識（practical knowledge）。
在數學語言相關教學能力表現上，本研究也發現，兩個國家的職前教師在思考影響學生理解數學語言的因素時，都缺乏能從數學語言角度切入分析的能力，尤以美國更為嚴重。臺灣職前教師表現並非皆優於美國，在選用能培養學生數學語言能力的教學活動上表現即較美國差，且有相當高比例職前教師僅聚焦於數學概念而非數學語言的培養。
此外，職前教師在描述其想法時，用詞侷限，不能明確、精準使用數學教育中使用的專門詞彙，從Skemp（1987）的角度，職前教師數學教育中的概念與承載它的語言連結，職前教師便能自由控制自己思想、與他人溝通，也能促進新概念的形成，職前教師關於數學教育中詞彙的使用乃反映其在師資培育學程中的培養情況（Blömeke et al., 2008），故而此現象值得師培界考量。

中文
王仲春、李元中、顧莉蕾、孫名符（1995）。數學思維與數學方法論。臺北市：建宏出版社。
任樟輝（1996）。數學思維論。南寧市：廣西教育出版社。
伍謙光（1995）。語義學導論。湖南省：湖南教育出版社。
吳秀萍（2004）。國中生對垂直、平行相關用語之理解研究（未出版碩士論文）。國立台灣師範大學，臺北市。
李士錡（2001）。PME：數學教育心理。上海：華東師範大學出版社。
李宇明（1997）。理論教育學教程。武漢：華中師範大學出版社。
林福來（1997）。教學思維的發展：整合數學教學知識的教材教法（I）。國科會專題研究計畫成果報告（No. NSC 86-2511-S-003-025）。臺北市：臺灣師大數學系。
徐芷儀（1999）。兩文三語: 語法系統比較。臺北市：臺灣學生。
徐烈炯（1995）。語義學。北京市：語文出版社出版。
張春興（1998）。張氏心理學辭典。臺北市：東華書局。
教育部（2008）。97年國民中小學九年一貫課程綱要。台北：作者。
陳仁輝、楊德清（2010）。臺灣、美國與新加坡七年級代數教材之比較研究。科學教育學刊，18（1），43-61。
陳新雄、竺家寧、姚榮松、羅肇錦、孔仲溫、吳聖雄等人（2005）。語言學辭典。臺北市：三民。
楊信彰（2005）。語言學概論。北京市：高等教育出版社。
葛本儀（2002）。語言學概論。臺北市：五南圖書出版股份有限公司。
謝國平（1998）。語言學概論。臺北市：三民。
謝豐瑞（2009）。中學數學教師專業發展指標之研究-子計畫四：中學教師數學教學能力專業發展研究。國科會專題研究計畫成果報告（NSC 96-2522-S-003-008-）。臺北市：國立臺灣師範大學。
謝豐瑞（2011）。21世紀數學教學跨國研究。國科會專題研究計畫成果報告（NSC 96-2522-S-003-021-MY2）。臺北市：國立臺灣師範大學。
謝豐瑞（2012a）。中學數學職前教師之數學教學知能。載於謝豐瑞（主編），臺灣數學師資培育跨國研究Taiwan TEDS-M 2008（119-142頁）。臺北：國立臺灣師範大學數學系。
謝豐瑞（2012b）。臺灣不同培育模式之中學數學職前教師數學教學知能。載於謝豐瑞（主編），臺灣數學師資培育跨國研究進階分析（159-191頁）。臺北：國立臺灣師範大學數學系。
謝豐瑞、王婷瑩（2012）。中學數學職前教師之數學知能。載於謝豐瑞（主編），臺灣數學師資培育跨國研究Taiwan TEDS-M 2008（93-117頁）。臺北：國立臺灣師範大學數學系。
謝豐瑞、楊志堅、施皓耀（2012）。中學數學職前教師在師資培育課程之學習機會。載於謝豐瑞（主編），臺灣數學師資培育跨國研究Taiwan TEDS-M 2008（143-169頁）。臺北：國立臺灣師範大學數學系。

 
西文
An, S., Kulm, G., & Wu, Z. (2004). The pedagogical knowledge of middle school, mathematics teachers in China and The U.S.. Journal of Mathematics Teacher Education, 7(2), 145-172.
Ball, D. L., Thames, M.H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407.
Barton, M. L., & Heidema, C. (2000). Teaching reading in mathematics: A supplement to “Teaching Reading in the Content Areas Teacher's Manual (2nd Ed.)”. Washington, DC: Office of Educational Research and Improvement.
Barwell, R. (2005a). Integrating language and content: Issues from the mathematics classroom. Linguistics and Education: An International Research Journal, 16(2), 205-218.
Barwell, R. (2005b). Language in the mathematics classroom. Language and Education, 19(2), 97-102.
Blömeke, S., Paine, L., Houang, R. T., Hsieh, F.-J., Schmidt, W. H., Tatto, M. T., Bankov, K., Cedillo, T., Cogan, L., Han, S.-I., Santillan, M., & Schwille, J. (2008). Future teachers’ competence to plan a lesson: first results of a six-country study on the efficiency of teacher education. ZDM Mathematics Education, 40(5), 749-762.
Bloomfield, L. (1933). Language. New York: Holt.
Bloomfield, L. (1939). Linguistic aspects of science. Chicago, Ill.: The University of Chicago press.
Boero, P., Douek, N., & Ferrari, P. L. (2002). Developing mastery of natural language: Approaches to theoretical aspects of mathematics. In L. D. English, M. B. Bussi, G. A. Jones, R. A. Lesh, & D. Tirosh (Eds.), Handbook of international research in mathematics education (pp. 241-268). N.J.: Lawrence Erlbaum.
Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education, 23(3), 194-222.
Cankoy, O. (2010). Mathematics Teachers' Topic-Specific Pedagogical Content Knowledge in the Context of Teaching a0, 0! and a÷0. Theory and Practice, 10(2), 749-769.
Capraro, R. M., Capraro, M. M., Parker, D., Kulm, G., & Raulerson, T. (2005). The mathematics content knowledge role in developing preservice teachers’ pedagogical content knowledge. Journal of Research in Childhood Education, 20(2), 102-118.
Carter, T. A., & Dean, E. O. (2006). Mathematics intervention for grades 5-11: Teaching mathematics, reading, or both? Reading Psychology, 27(2-3), 127-146.
De Corte, E., & Verschaffel, L. (1991). Some factors influencing the solution of addition and subtraction word problems. In K. Durkin & B. Shire (Eds.), Language in mathematical education: Research and practice (pp. 117-130). Milton Keynes: Open University Press.
De Corte, E., Verschaffel, L., & De Win, L. (1985). The influence of rewording verbal problems on children's problem representations and solutions. Journal of Educational Psychology, 77(4), 460-470.
Devitt, M., & Sterelny, K. (1999). Language and reality: An introduction to the philosophy of language. Mass: MIT Press.
Dewey, J. (1991). How we think. NY: Prometheus Books.
Durkin, K., & Shire, B. (1991). Language in mathematical education: Research and practice. Philadelphia: Open University Press.
Educational Testing Service (2010). Mathematics: Pedagogy (0065). Princeton, NJ: Author. Retrieved from http://www.ets.org/Media/Tests/PRAXIS/pdf/0065.pdf
Ellerton, N. F., & Clarkson, P. C. (1996). Language factors in mathematics teaching and learning. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 987-1033). Boston: Kluwer Academic Publishers.
Felbrich,A., Kaiser, G., & Schmotz, C. (2012). The cultural dimension of beliefs: an investigation of future primary teachers’ epistemological beliefs concerning the nature of mathematics in 15 countries. ZDM – The International Journal on Mathematics Education, 44(3), 355-366. doi: 10.1007/s11858-012-0418-x
Ferrari, P. L. (2004, July). Mathematical language and advanced mathematics learning. Paper presented at 28th Conference of International Group for the Psychology of Mathematics Education, Bergen, Norway.
Geertz, C. (1984). “From the native’s point of view”: On the nature of anthropological understanding. In R. A. Shweder & R. LeVine (Eds.), Culture theory: Essays on mind, self, and emotion (pp. 123-136). Cambridge, England: Cambridge University Press.
Gough, J. (2007). Conceptual complesxity and apparent contradictions in mathematics language. Australian Mathematics Teacher, 63(2), 8-15.
Hackett, K., & Wilson, T. (1995). Improving writing and speaking skills using mathematical language. Retrieved from ERIC database. (ED386747)
Halliday, M. A. K. (1978). Language as social semiotic: The social interpretation of language and meaning. Baltimore: University Park Press.
Han, Y., & Ginsburg, H. P. (2001). Chinese and English mathematics language: The relation between linguistic clarity and mathematics performance. Mathematical Thinking and Learning, 3(2-3), 201-220.
Herbel-Eisenmann, B. A. (2002). Using student contributions and multiple representations to develop mathematical language. Mathematics Teaching in the Middle School, 8(2), 100-105.
Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.
Hill, H. C., Sleep, L., Lewis, J. M., & Ball, D. L. (2007). Assessing teachers' mathematical knowledge: What knowledge matters and what evidence counts? In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 111-155). Charlotte, NC: Information Age Publishing.
Hsieh, F. J., Wang, T. Y., & Wu, X. P. (2008, July). Understanding the teachers’ use of sentences in mathematics classroom. Paper presented at 11th International Congress on Mathematical Education, Monterrey, Mexico.
Hsieh, F.-J., Lin, P.-J., & Wang, T.-Y. (2012). Mathematics related teaching competence of Taiwanese primary future teachers: Evidence from the TEDS-M. ZDM – The International Journal on Mathematics Education, 44(3), 277-292. doi: 10.1007/s11858-011-0377-7
Koirala, H. P., Davis, M., & Johnson, P. (2008). Development of a performance assessment task and rubric to measure prospective secondary school mathematics teachers’ pedagogical content knowledge and skills. Journal of Mathematics Teacher Education, 11(2), 83-88.
Krutetskii, V.A. (1976). The psychology of mathematical abilities in schoolchildren (J. Teller, Trans.), Chicago: The University of Chicago Press. (Original work published 1968).
Laborde, C. (1990). Language and mathematcis. In P. Nesher & J. Kilpatrick (Eds.), Language and comprehension (pp. 53-69). New York: Cambridge University Press.
Lager, C. A. (2006). Types of mathematics-language reading interactions that unnecessarily hinder algebra learning and assessment. Reading Psychology, 27(2-3), 165-204.
Langacker, R. W. (1967). Language and its structure: Some fundamental linguistic concepts. New York: Harcourt Brace Jovanovich.
Learning Mathematics for Teaching. (2006). A coding rubric for measuring the mathematical quality of instruction (Technical report LMT1.06). Ann Arbor, MI: University of Michigan, School of Education.
Leech, G. N. (1974). Semantics. Harmondsworth: Penguin.
Leung, F. K. S. (2006). Mathematics education in East Asia and the West: Does culture matter? In F. K. S. Leung, K.-D. Graf, & F. J. Lopez-Real (Eds.), Mathematics education in different cultural traditions - A comparative study of the East Asia and the West (pp. 195-211). New York: Springer.
Li, Y., & Ginsburg, M. B. (2006). Classification and framing of mathematical knowledge in Hong Kong, Mainland China, Singapore, and the United States. In F. K. S. Leung, K.-D. Graf, & F. J. Lopez-Real (Eds.), Mathematics education in different cultural traditions - A comparative study of the East Asia and the West (pp. 195-211). New York: Springer.
Lightfoot, D., & Fasold, R. W. (2006). The structure of sentences. In R. W. Fasold & J. Connor-Linton (Eds.), An introduction to language and linguistics (pp. 97-135). New York: Cambridge University Press.
Marr, B. (2000, July). How can they belong if they cannot speak the language? Enhancing students' language use in the adult mathematics classroom. Paper presented at 7th International Conference on Adults Learning Mathematics, Medford, MA.
Mosteller, F., & Tukey, J. W. (1977), Data Analysis and Regression. Reading, MA: Addison-Wesley.
National Governors Association Center for Best Practices, Council of Chief State School Officers (2010). Common core state standards for mathematics. Washington D.C: National Governors Association Center for Best Practices, Council of Chief State School Officers.
NCATE/NCTM Program Standards (2003). Standards for secondary mathematics teachers. Retrieved from http://www.ncate.org/LinkClick.aspx?fileticket=ePLYvZRCuLg%3d&tabid=676
Niss, M. A. (2003). Mathematical competencies and the learning of mathematics: the Danish KOM project. In Gagatsis, A., & Papastavridis, S. (Eds.), 3rd Mediterranean Conference on Mathematical Education - Athens, Hellas 3-4-5 January 2003 (pp. 116-124). Athen: Hellenic Mathematical Society.
Patton, M. (2002). Qualitative research & evaluation methods (3rd ed.).Thousand Oaks, CA: Sage.
Perry, B., Wong, N.-Y., & Howard, P. (2006). Comparing primary and secondary mathematics teachers’ beliefs about and mathematics teaching in Hong Kong and Australia. In F. K. S. Leung, K.-D. Graf, & F. J. Lopez-Real (Eds.), Mathematics education in different cultural traditions - A comparative study of the East Asia and the West (pp. 21-46). New York: Springer.
Pimm, D. (1987). Speaking mathematically: Communication in mathematics classrooms. New York: Routledge.
Pimm, D. (1995). Symbols and meanings in school mathematics. New York: Routledge.
Portner, P. (2006). Meaning. In R. W. Fasold & J. Connor-Linton (Eds.), An introduction to language and linguistics (pp. 137-168). New York: Cambridge University Press.
Raiker, A. (2002). Spoken language and mathematics. Cambridge Journal of Education, 32(1), 45-60.
Robins, R. H. (1997). A short history of linguistics (4nd ed.). New York: Longman.
Rubenstein, R. N., & Thompson, D. R. (2001). Learning mathematical symbolism: Challenges and instructional strategies. Mathematics Teacher, 94(4), 265-271.
Saenz-Ludlow, A., & Walgamuth, C. (1998) Third Graders interpretations of equality and the equal symbol. Educational Studies in Mathematics, 35(2), 153-187.
Sapir, E. (1921). Language: An introduction to the study of speech. New York: Harcourt.
Saussure, F. D. (1966). Course in general linguistics. New York：McGraw-Hill.
Scheffler, I. (1997). Symbolic worlds: Art, science, language, ritual. New York: Cambridge University Press.
Schmidt W. H., Blömeke, S., Tatto, M. T., Hsieh, F.-J., Cogan, L., Houang, R. T., Bankov, K., Santillan, M., Cedillo, T., Han, S.-I., Carnoy, M., Paine, L., & Schwille, J. (2011). Teacher education matters: A study of middle school mathematics teacher preparation in six countries. NY: Teacher College Press.
Schön, D. A. (1983) The reflective practitioner: how professionals think in action. USA: Basic Books.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
Silver, E. A. (1998). Improving mathematics in middle school: Lessons from TIMSS and related research. Washington, DC: U.S. Department of Education.
Siu, M. K. (2009). Mathematics education in East Asia from antiquity to modern times. In K. Bjarnadottir, F. Furinghetti, & G. Schubring (Eds.), Dig where you stand: Proceedings of the conference on on-going research in the history of mathematics education (pp. 197-208). Reykjavik: School of Education of University of Iceland.
Skemp, R. R. (1987). The psychology of learning mathematics. New York: Routledge.
Stigler, J. W., Gallimore, R., & Hiebert, J. (2000). Using video surveys to compare classrooms and teaching across cultures: Examples and lessons from the TIMSS video studies. Educational Psychologist, 35(2), 87-100.
Street, B. (2005). The hidden dimensions of mathematical language and literacy. Language and Education, 19(2), 135-140.
Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Rowley, G., Peck, R., Bankov, K., Rodriguez, M., & Reckase, M. (2011). The teacher education study in mathematics (TEDS-M): Policy, practice, and readiness to teach primary and secondary mathematics. New York: Springer.
Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Rowley, G., Peck, R., …Holdgreve-Resendez, R. (2012). Policy, practice, and readiness to teach primary and secondary mathematics in 17 countries. Amsterdam: Multicopy.
Tatto, M. T., Schwille, J., Senk, S., Rodriguez, M., Bankov, K., Reckase, M, D., Ingvarson, L., Peck, R., & Rowley, G., Dumais, J., Carstens, R., Brese, F., Meinck, S. (2009). Teacher education study in mathematics (TEDS-M): Technical summary. East Lansing, MI: Teacher Education International Study Center, College of Education, Michigan State University.
Teubal, E., & Nesher, P. (1991). Order of mention vs order of events as determining factors in additive word problems: A developmental approach. In K. Durkin & B. Shire (Eds.), Language in mathematics: Research and practice (pp. 131-139). Milton Keynes: Open University Press.
Triandis, H. C. (1995). Individualism and collectivism. San Francisco: Westview Press.
Warren, E. (2006). Comparative mathematical language in the elementary school: A longitudinal study. Educational Studies in Mathematics, 62(2), 169-189.
Willingham, D.T. (2005, Summer). Do visual, auditory, and kinesthetic learners need visual, auditory, and kinesthetic instruction? American Educator, 29(2), 31-35.
Wilson, S., Shulman, L., & Richert, A. (1987). "150 different ways of knowing":Representations of knowledge in teaching. In J. Calderhead (Ed.), Exploring teachers'thinking (pp. 104-123). Eastbourne, England: Cassell.
Werner, H., & Kaplan, B. (1964). Symbol formation: An organismic developmental approach to language and the expression. New York: Wiley.
Zack, V. (1999). Everyday and mathematical language in children's argumentation about proof. Educational Review, 51(2), 129-146.
Zevenbergen, R. (2001). Language, social class and underachievement in school mathematics. In P. Gates (Ed.), Issues in mathematics teaching (pp. 38-50). New York: RoutledgeFalmer.